In a triangular triangle, one leg is 3 times larger than the other, and the hypotenuse is 10 cm, find the smaller leg.

Let us denote by a the length of that of the two legs of a given triangle with one right angle, which is large.

In the initial data for this task, it is reported that one of the legs is three times larger than the other, therefore, the length of the length of that of the two legs of this triangle, which is the smallest, is a / 3 cm.

Since the hypotenuse of this triangle has a length equal to ten centimeters, we can draw up the following equation:

a² + (a / 3) ² = 10²,

solving which, we get:

a² + a² / 9 = 100;

10а² / 9 = 100;

a² / 9 = 100/10;

a² / 9 = 10;

(a / 3) ² = 10;

a / 3 = √10;

a = 3√10.

Find the smaller leg:

3√10 / 3 = √10.

Answer: √10 cm.